Q1. (a) Given the function f(x) = 2x3 + 4 find (1) /(7), GD) f(-0.5). (3 marks) (b) Calculate /(4r + 5) when f(x) = c'. Write down the corresponding expression for /(4r + 2) - /(x). (4 marks) (c) If f(x) = 4x + 2 and g(x) = r + 3 find (go/)(r). (3 marks) (d) Consider the function given by g(x) = r' +5, -2 c $ 3. (i) State the domain of the function. (ii) Plot the graph of the function. (iii) Deduce the range of the function from the graph. (State the input and output table.) (5 marks) Q2. (a) Find the inverse of each of the following functions: (i) /(x) = 7 + 5x, (ii) /(x) = 3r. (5 marks).Q3. (a) For the matrices A = 3 4 and B = find, where possible, 3 2 (1) AT, (ID) AB. (5 marks) (b) Use expansion along the first row to find A (5 marks)Q4. la} Find the inverse of the following matrices using determinants if possible: til A. '1 '1 _ 2 2 ' .. l I In] B = [a 1] . {5 marks} [bl Ill Using Cramer's rule obtain the solution to the following set of equations: h+y=8 3.x4u'=5. {5 marks} Q5. {a} Solve the following system of equations using inverse matrix method (AX = Band X = A"B}: 21+3y=3 fu+4y=l {5 marks) (5 marks) (b) Diffie-Hellman key exchange is based on the difficulty of solving the Discrete Logarithm Problem. For instance, Alice and Bob agree on a prime number p = 7 and a number (base) g = 4. This is the public aspect of the system. Using this algorithm, find the kprivate- (5 marks) Q6. (a) Solve the following using Gauss elimination method: 201 + 12 - 13 = 0 m+: = 4 (5 marks) (b) Find the inverse of the matrix from (a) using the same method and steps. (5 marks) Questions continue on next page 3